Worst position by team

[JohnTurney]

I'll start

Bears QB, as noted, if Jim McMahon's 1985 season can be considered as one of best, then it's lacking

Rams TE. Lance Kendricks has 17 career TD rec. One more ties franchise career record. Gronk had 17 alone in 2011.

[JWL]

Possibilities-
kickoff returner- Buccaneers
running back- Buccaneers

[ChrisBabcock]

Patriots - RB
Career yardage leader being Sam Cunningham of whom 99% of casual fans would say "who?"

Bengals - defensive line
Although definitely a strength of the team the last 5 years or so.

Chargers - CB

[JeffreyMiller]

For the Buffalo Bills, it's tight end. Only two players have been voted to participate in a pro bowl, and both of those happened at least 50 years ago--Ernie Warlick (62, 63, 64) and Paul Costa (66). Pretty sad ...

[BD Sullivan]

Browns: Cornerback

[74_75_78_79_]

Browns: Cornerback

How about Minnifield/Dixon?

[Citizen]

The only positions at which the Packers aren't represented in the PFHoF are tight end and punter, so I guess one of those.

[bachslunch]

For the Buffalo Bills, it's tight end. Only two players have been voted to participate in a pro bowl, and both of those happened at least 50 years ago--Ernie Warlick (62, 63, 64) and Paul Costa (66). Pretty sad ...

Warlick's career is unusual -- didn't start playing American pro football until age 30 (spent five years prior in the CFL), then made the AFL all star game all four years he was there (includes his final season in 1965 when the entire Bills title team played all stars from the rest of the AFL).

[JuggernautJ]

I think we can discount Punter and Kicker as positions for this discussion. Likewise Return Specialists as all these categories are poorly represented in the Hall of Fame and are secondary to the starting positions.

If we look at the Hall as a criterion for this discussion it will quickly become evident that some teams' weak points are very different than others.

For instance (and if I am not mistaken) the Raiders have Hall of Famers at virtually every position:
Center: Otto
Guard: Upshaw
Tackle: Shell
TE: Casper
WR: Biletnikoff
RB: Allen
QB: Stabler
DT/DE: Long
LB: Hendricks
DB: Brown

I guess, if we take long as primarily a DE then that leaves DT as the only position for the Raiders not in the Hall (they even have a Punter in Guy and a Kicker in Blanda).
But I wouldn't want to have to tell Otis Sistrunk or Chester McGlocktin that they were the team's weak link...

[BD Sullivan]

Browns: Cornerback

How about Minnifield/Dixon?

That's one of the few times that they had any consistent level of strong play in that area and that was for only about five years--out of 68.